⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣴⣶⣦⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣄⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⣄⣀⣀⣀⣀⠀⠀⠀⣷⡇⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣿⡿⠋⠻⣿⣷⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣍⣐⠻⢦⣄⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣦⠀⠀⡏⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠄⠀⠀⠻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡙⢷⣄⠀⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⠿⠀⢠⡽⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠹⣦⠀⠀ ⠀⠀⢸⣿⣿⣿⡿⣿⣿⣧⢠⡿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢩⡇⠀ ⠀⠀⠈⠛⠉⠉⠀⠋⣉⣽⠟⡱⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣶⠀ ⠀⢀⣀⣀⣀⣤⣖⠾⢋⣵⡎⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⣠⣾⣄⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⠉⠉⠉⣿⣿⣿⣿⣿⠀⣿⠀ ⢸⠋⣭⣭⣭⣥⣴⣾⣿⣿⡇⠀⠈⠉⠉⠉⠉⠉⠉⠉⢉⣽⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⢿⣿⣯⡉⠀⠀⠀⣿⣿⣿⣿⣿⠀⣿⠀ ⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠈⠻⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠙⢽⢿⣿⣦⡀⠀⠀⠀⠀⠀⢸⠀⣿⠀ ⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⢀⣼⡿⠋⠀⠀⠀⣠⣶⣄⠀⠀⠀⠀⠙⢽⢿⣿⣦⡀⠀⠀⠀⢸⠀⣿⠀ ⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠈⠻⣷⣄⣴⡿⠋⠀⠀⠀⣠⣾⡿⠛⢿⣷⣄⠀⠀⠀⠀⠙⢝⢿⣿⣦⡀⠀⢸⠀⣿⠀ ⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⣷⣄⠀⠀⠀⠀⠀⠈⠿⠋⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⠀⠑⢟⣿⣿⣯⣹⠀⣿⠀ ⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠋⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⢠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠑⢟⣿⣿⣦⣿⠀ ⢸⠀⡇⠀⠀⠀⠀⠀⠀⢠⣾⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣏⠀⠀⠀⠀⠀⢈⣿⡷⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⢠⣼⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢝⢿⣿⡆ ⢸⠀⡇⠐⠀⠀⠀⡀⠀⠘⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣷⣄⠀⢀⣴⡿⠋⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠒⣩⣿⣿⠇ ⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇⠙⢿⣿⣄⡀⣀⡀⠀⠀⠀⠀⠀⠀⠙⢿⣷⡿⠋⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⢀⣴⡿⢋⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⣷⠀ ⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠒⠻⠒⠒⠒⣀⣶⡿⠋⠀⠀⠀⠀⠀⢀⣴⡿⣫⠎⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠃⣿⠀ ⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡿⠋⠀⠀⠀⠀⠀⢀⣴⡿⣫⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⠋⢸⠀⣿⠀ ⢸⠀⡇⠀⠀⠀⠀⠀⢠⢳⡇⠀⠀⠀⠀⠀⠈⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀⢰⣿⣯⡀⠀⠀⠀⠀⢀⣴⡿⣫⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⡿⠋⠀⠀⢸⠀⣿⠀ ⢸⢀⡇⠀⠀⠀⠐⢒⠋⣄⢣⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣄⠀⠀⠀⠀⠈⠻⣿⣿⣦⡀⢀⣴⡿⣫⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⡡⠋⠀⠀⠀⠀⢸⠀⣿⠀ ⢸⠘⡇⠀⠀⠀⢀⠋⣼⣿⡄⢣⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣄⠀⠀⠀⠀⠈⠻⣿⣿⡿⣫⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⣿⠋⠀⠀⠀⠀⠀⠀⢸⡆⣿⠀ ⢸⠀⡇⠀⠀⢀⠏⣼⣿⣿⣿⡄⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣄⠀⠀⠀⠀⠈⠻⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⡡⠊⢸⠀⠀⠀⠀⠀⠀⠀⢸⡄⣿⠀ ⢸⠀⡇⠀⢀⠎⣼⣿⣿⣿⣿⣿⡄⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⡡⠊⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀ ⢸⠀⡇⢀⠎⣴⣿⣿⣿⣿⣿⣿⣿⡄⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡟⡡⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀ ⢸⢰⣇⠎⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡟⡣⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀ ⢸⢸⠏⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣄⠀⠀⠀⢠⣼⣿⡿⡫⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀ ⢸⢸⡶⠿⠿⠿⠿⠿⠿⠿⡏⠉⠹⠿⠿⠿⡌⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣄⣴⣿⡿⡫⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀ ⠸⡏⣇⣀⣀⣀⣀⣀⣀⣀⣃⣀⣀⣀⣀⣤⣼⡌⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⡿⠯⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢱⠿⠀ ⠸⣣⢣⡤⠤⠤⠤⠤⠤⠤⡤⠤⠤⠤⠤⠤⠤⠤⠬⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⣘⡇⠀ ⠀⠹⣣⠳⡀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⣼⠟⠀⠀ ⠀⠀⠙⢵⢌⠢⣄⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣠⠔⡡⡾⠊⠀⠀⠀ ⠀⠀⠀⠀⠙⠻⣶⡭⣓⣒⡒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢚⣒⣚⢭⣴⠟⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀